On the Cusum test for parameter changes in garch(1,1) Models

The Cusum Test for Parameter Change in Regression Models with ARCH Errors

“…Therefore it is worth to investigate the asymptotic behavior of the residual cusum test in ARCH models. Although the present paper was originally motivated to improve Kim et al's (2000) test in the GARCH(1, 1) model, we consider the cusum test in a more general class of models including regression models with infinite order ARCH errors.…”

“…In Section 2, we introduce the residual cusum test in regression models with infinite order ARCH models that include the GARCH model, and show that its limiting distribution is the sup of a Brownian bridge. In Section 3, we perform a simulation study to compare our test with Kim et al's (2000) test in GARCH(1, 1) models. The result indicates that our method outperforms their cusum test.…”

“…It is shown that the limiting distribution of the residual cusum test statistic is the sup of a Brownian bridge. Through a simulation study, it is demonstrated that the proposed test circumvents the drawbacks of Kim et al's (2000) cusum test. For illustration, we apply the residual cusum test to the return of yen/dollar exchange rate data.…”

“…In fact, Kim et al (2000) considered to apply the cusum test to GARCH(1, 1) models taking account of the fact that the variance is a functional of GARCH parameters, and their change can be detected by examining the existence of the variance change. Although this reasoning was correct, it turned out that the cusum test suffers from severe size distortions and low powers.…”

Testing the exchange rate data for the parameter change based on ARMA-GARCH model

“…Their test is reviewed in Section 2. For the change points test in GARCH models, we refer to Kim et al (2000), Lee et al (2004), and Berkes et al (2004).…”